Refining connected topological group topologies on Abelian torsion-free groups. (English) Zbl 0895.54023

The authors develop a technique for refining certain topological groups. The main result of the paper is:
Theorem. Let \(G\) be a connected Abelian torsion-free group with weight less than or equal to \(\aleph_1\) and cellularity less than or equal to \(\aleph_0\). Then \(G\) admits a strictly finer connected topological group topology satisfying the same cardinality restrictions.
Reviewer: R.Cowen (Gaborone)


54H11 Topological groups (topological aspects)
22A05 Structure of general topological groups
54D05 Connected and locally connected spaces (general aspects)
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
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